Thursday, August 18, 2016


The current idea in many modern modelling systems (at catchment scale) is that the hydrology of control volumes can be reduced to a set of interconnected reservoirs (Fenicia et al., 2008; Tague et al., 2010; Clark et al., 2008; Hrachowitz et al., 2013). Each one of these reservoir can be thought as “well mixed”, meaning that each water reservoir acts like a chemical reactor where all what comes in is uniformly distributed across the reservoir and perfectly mixes (and instantaneously too) with everything already present. Some of these reservoirs have a geographical identification (as happened in the geomorphologic unit hydrograph, eg. Rinaldo and Rodriguez-Iturbe, 1996), some others have a functional reason and we could call them “embedded”, or with no-geographical reference. They are used especially to disentangle processes, to attribute the right travel time to water, and, more prosaically, to get right quantitative adjustements to the various outputs, discharge, first of all. 

This way of working is quite necessary (but remind Todini’s adage: first they had a linear reservoir -Sherman, 1932 -, then they introduced a sequence of linear reservoirs - Nash, 1957, after, they made the reservoirs non linear, Dooge, 1959; finally was a mess, Sagawara, 1967) but the separation (or the composition, it depends from the point of view) of the domain in parts is somewhat that remains to be demonstrated.

In using these simplifications  nobody of the researchers mentioned goes through a direct simplification of coupled (hydrological) equations at the finer scale and coarse grain them^1, but directly adopts the paradigm of reservoirs and validate it, nowadays technologically, by using a set of GOFs (goodness of fit) indicators. 

This system is, IMO, intrinsically weak but I, like the others, adopted it. A statistical theory is missing, and I believe that it will arise from the travel time theories

In the revamp of  these reservoirs' theories, the attention to the spatial distribution of the reservoirs should find again its place. Distinguishing, “vertically”, reservoirs as canopy, surface, vadose zone and groundwater storage is a necessity that is widely recognised and should be deployed. Reservoirs “lateral” aggregation (by using convolutions or following new paradigms) is the follow up (see also Rigon et al., 2016a). Embedded chains of reservoirs should be also necessary, as invoked by those who study small catchments experimentally (e.g. Birkel, 2011). All should be investigated carefully, and complexity added after implementing “ad hoc” experiments, or using appropriate datasets. 

This scenery would not be complete if these models would limit themselves to consider just the forecasting of discharges. They should also convey a reasonable set of processes to close the water budget. Next would be to include appropriate simplifications of the energy budget, a necessary companion. The latter, however, was never tried so far in coarse grained models.


^1 Perhaps Paolo Reggiani et al, 1998 tried it in a generic way, making experience on Gray’s previous work, and Todini did it, his own way with Topkapy, i.e. Liu and Todini, 2002; see also Todini, 2007 and my talk here. Paolo's work is certainly to be reconsidered.


Birkel, C., Soulsby, C., & Tetzlaff, D. (2014). Developing a consistent process-based conceptualization of catchment functioning using measurements of internal state variables. Water Resources Research, 50(4), 3481–3501.

Clark, M. P., A. G. Slater, D. E. Rupp, R. A. Woods, J. A. Vrugt, H. V. Gupta, T. Wagener, and L. E. Hay (2008), Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models, Water Resour. Res., 44, W00B02, doi:10.1029/2007WR006735.

Dooge J,  (1959) - This reference was suggested by Ezio Todini, but I did not find it (the one talking of non-linear reservoirs).

Fenicia F, Savenije HHG, Matgen P, Pfister L, 2008. Understanding catchment behavior through stepwise model concept improvement. Water Resour. Res. 44(1): W01402. ISSN 0043-1397. doi:10.1029/2006WR005563. 

Gray, W., Lijennse, A, Kolar, R.L, Blain, C.A., Mathematical tools for changing spatial scales in the analysis of physical systems, CRC Press, Boca Raton, 1994

Hrachowitz, M., Savenije, H., Bogaard, T. A., Tetzlaff, D., & Soulsby, C. (2013). What can flux tracking teach us about water age distribution patterns and their temporal dynamics? Hydrology and Earth System Sciences, 17(2), 533–564.

Liu and Todini (2002), Towards a comprehensive physically-based rainfall-runoff model, Hydrology and Earth System Sciences, 6(5), 859–881

Nash, J.E., 1958, The form of the instantaneous unit hydrograph, IUGG General Assembly of Toronto, Vol III, IAHS pub. no. 45, 1141-121. 

Reggiani, P., M. Sivapalan, and S. M. Hassanizadeh (1998), A unifying

Rinaldo A & Rodríguez-Iturbe I, 1996. Geomorphological theory of the hydrological response. Hydrol. Process. 10(6): 803–829. ISSN 1099-1085. doi:10.1002/(SICI)1099- 1085(199606)10:6<803::AID-HYP373>3.0.CO;2-N. 

Rigon R., Bancheri M., Formetta G., & de Lavenne, A. (2015). The geomorphological unit hydrograph from a historical-critical perspective. Earth Surface Processes and Landforms, n/a–n/a.

Rigon R., Bancheri M, Green T., Age-ranked hydrological budgets and a travel time description of catchment hydrology,Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-210, in review, 2016.

Sherman, L. K., Streamflow from rainfall by the unit hydrograph method, Eng. News-Record 108, 501-505, 1932. 

Sugawara, 1967, The flood forecasting by a seried storage type model, IAHS Publication no. 85, 1-6

Tague, C., & Dugger, A. L. (2010). Ecohydrology and Climate Change in the Mountains of the Western USA - A Review of Research and Opportunities. Geography Compass, 4(11), 1648–1663.

Todini, E. (2007). Hydrological catchment modelling: past, present and future. Hess, 11(1), 468–482.


  1. Thank you for the great post and references! I think that this reservoir-based paradigm is a trap of parsimony. If clean and simple models works well (e.g. HBV, GR4J etc.) in many cases, why we have to spend our lives for complex LSM schemes development (under the condition that we need only high Nash-Sutcliffe metric)?

    1. Thank you for appreciation, you make a point. However, my position as researcher is that we should understand because certain models work well and other less. I this I recognise myself in Klemeš and Kirchner (Klemeš, 1986; Kirchner, 2006). Besides, in my experience, the claim that a model work well is often overrated. NS is not a very discriminant indicator, and relevant part of the hydrograph remain not well described by too simple models.
      Another experience is that we seldom do "forecasting". As hydrologist, we often do past-casting, meaning that we forecast past events, and rarely we challenge the real forecast, i.e. predicting future events (which, in turn, is made difficult by lack of appropriate precipitation forecasting). That's why I remain usually not so happy with too simple model. As Einstein (?) says, keep it simple, but not too simple !
      As an engineer, however, I try to keep modelling it as much simple as possible, and maintain my desiderata feasible.


      Kirchner, J. W. (2006), Getting the right answers for the right reasons: Linking measurements, analyses, and models toadvance the science of hydrology, Water Resour. Res., 42, W03S04, doi:10.1029/2005WR004362.

      Klemeš, V. (1986). Dilettantism in Hydrology: Transition or Destiny ? Water Resources Research, 22(9), 177S–188S.

    2. I forgot to add that some complexity in modelling is "a place card" for modelling other processes than discharge (as, for instance, evapotranspiration or recharge or soil moisture content) which are becoming more and more a request by real life applications

    3. Thanks a lot for a detailed answer! Your next post about JGRASS underlines strong need for another water balance components prediction too - and for me, it is a great place for model improvements. Dr. Fenicia shows (somewhere) how modellers can fool themselves - we obtain good NS, but in the same time we have crazy behavior of our reservoirs. Thanks a lot for your posts!

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